Chapter 19
Downloaded via UNIV OF TEXAS AT EL PASO on October 28, 2018 at 17:58:27 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
Aluminum Magnetic Shielding Tensors and Electric Field Gradients for Aluminum(I) Hydride, Aluminum(I) Isocyanide, and the Aluminum(I) Halides: Ab Initio Calculations Myrlene Gee and Roderick E. Wasylishen Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4J3, Canada
Ab initio calculations of aluminum nuclear magnetic shielding tensors for aluminum(I) hydride, aluminum(I) isocyanide and the aluminum(I) halides are presented. Accurate experimental Al shielding tensors available for AlCl and AlNC from recent spin-rotation data provide a stringent test of the ab initio calculations. For these two molecules, RHF calculations employing large basis sets provide shielding tensors which are in good agreement with experiment. The calculations indicate that the Al spin-rotation constant for AlH is relatively large, C = 295 kHz. Calculated boron and gallium shielding tensors of the group 13 hydrides and halides exhibit trends analogous to the corresponding aluminum tensors. For example, the group 13 nucleus of the hydrides is least shielded, while that of the fluoride is most shielded. In all cases, the calculated B, Al and Ga shieldings perpendicular to the bond axis are found to correlate with the HOMO -LUMO gap. The component of the shielding tensor along the bond axis is insensitive to substituent and approximately equal to thefree-atomvalue: 202.0 ppm for B, 789.9 ppm for Al and 2638.6 ppm for Ga. Calculated Al quadrupolar coupling constants(C )for AlF, AlCl and AlNC agree very well with experimental values. For AlH, the calculated values of C are approximately -46 MHz while the reported experimental value is -36.72 MHz. This discrepancy may be due, in part, to the neglect of the Al spin-rotation interaction in the analysis of the hyperfine structure in the high-resolution microwave spectrum of AlH. 27
27
27
Q
Q
27
Aluminum N M R spectroscopy is a well-established technique for the characterization of solid materials such as ceramics, cements, glasses and zeolites (1-4). It has also been used extensively to investigate aluminum complexes in aqueous and non-aqueous solutions (5,6). The widespread use of A1 (/= 5/2) N M R can be attributed to its favorable N M R properties: a natural abundance of 100%, a fairly large nuclear magnetic moment and a relatively small nuclear quadrupole moment. Isotropic aluminum chemical shifts are available for hundreds of compounds and from these data it is clear that the chemical shift range is approximately 300 ppm (5, 6). In spite of this significant range, orientation27
© 1999 American Chemical Society Facelli and de Dios; Modeling NMR Chemical Shifts ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
259
260 dependent aluminum chemical shifts have only recently been unambiguously character ized. Anisotropic aluminum chemical shifts have been reported for sapphire (a-A1 0 ) ( 7), aluminum trichloride phosphoryl trichloride (A1C1 OPC1 ) (8) and a series of pseudooctahedral aluminum complexes (9). While A l N M R studies of stationary powder samples provide information about the relative orientation of the aluminum shielding and electric field gradient (EFG) tensors, information concerning the orientation of these tensors in the molecular frame is generally not available. However, reliable firstprinciples calculations of shielding and E F G tensors may be used to suggest likely orientations of these tensors in the molecular framework. Before tackling complex sys tems, it is important to establish the accuracy of ab initio methods for small molecules. With this goal in mind, the ab initio results for aluminum(I) hydride, aluminum(I) isocyanide and the aluminum® halides are presented. For A1C1 and A1NC, the calculated magnetic shielding tensors can be compared to experimental values derived from A l spin-rotation data (vide infra). For comparative purposes, calculated boron and gallium magnetic shielding tensors for the group 13 hydrides and halides are also presented. Finally, Al nuclear quadrupolar coupling constants calculated for A1H, A1F, A1C1 and A1NC are compared with accurate experimental values obtained from high-resolution microwave spectroscopy. One of the main benefits of comparing calculated and experi mental A l shielding and quadrupolar coupling data for these simple linear molecules is that the experimental data are obtained for "isolated" molecules in the gas phase. Further more, it is straightforward to correct calculated shielding and quadrupolar coupling data for rovibrational averaging. 2
3
3
3
2 7
2 7
27
27
Chemical Shielding N M R spectroscopists generally measure the chemical shift, δ, which is defined by equation 1:
δ
=
V s a m p l e
~
V r e f
χ 10
v
6
*
σ
, ref
ο
, sample
v
(1) '
ref
where v and v are the resonancefrequenciesof the sample and the reference respec tively; o and o are their respective nuclear magnetic shielding constants. The A1(H 0) cation of 0.1 M Al(N0 ) (aq) serves as a chemical shift reference for A l NMR studies. The aluminum absolute shielding constant for A1(H 0) is not known but ab initio calculations indicate a value of approximately 612 ppm (10). Experimental tech niques for measuring absolute shielding constants (i.e., relative to the bare nucleus) have been summarized (11,12). If accurate nuclear spin-rotation data are available for one or more molecules containing the nucleus of interest, reliable "experimental" absolute shielding constants can be determined. For A1, accurate spin-rotation constants are only available for A1C1 and A1NC. In general, nuclear magnetic shielding is described by a second-rank tensor. For linear molecules, only two components are unique: o„, the shielding when the C-axis of the molecule is parallel to the applied magnetic field, and o for the perpendicular orien tation. The isotropic shielding constant is given by o =( o +2o J/3 and the span, Ω, of the shielding tensor is | o - σ |. sample
sample
ref
ref
3+
2
2 7
6
3
3
3+
2
6
27
x
iso
u
l(
χ
Facelli and de Dios; Modeling NMR Chemical Shifts ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
261
It is often convenient to describe the shielding at a particular nucleus as arising from two mechanisms, as originally proposed by Ramsey (13): +σ
ά
ο = σ
ρ
(2)
d
The diamagnetic portion of the shielding tensor, o , depends only on the ground electronic state of the molecule, whereas the paramagnetic part, σ , depends on both the ground and excited electronic states of the molecule. Because virtual molecular electronic states must be accurately represented, the calculation of reliable shielding tensors remains a chal lenging problem. Generally, the inclusion of electron correlation together with highly polarized basis sets is essential for reliable ab initio calculations of shielding tensors. With the currently available technology, such demanding calculations are generally feasible only for moderately small molecules. The current status of ab initio magnetic shielding calculations has been reviewed recently (14-17). It has been known for many years that information about the paramagnetic term can be derived from experimental spin-rotation tensors (18). Nuclear spin-rotation tensors are measured using molecular beam magnetic resonance (MBMR) and molecular beam electric resonance (MBER) methods as well as high-resolution microwave spectroscopy (19,20). Ramsey (13,18) and Flygare (21,22) have shown how the diagonal components of the spin-rotation tensor are related to the paramagnetic shielding tensor. For a linear molecule, the shielding component perpendicular to the molecular axis is given by: ρ
-m C ο
P-i- + o
-
d
(3)
t a t o m
Img^B
v
}
where m and m are the masses of the electron and proton, respectively, g is the nuclear g- value, C is the perpendicular component of the spin-rotation tensor, Β is the molecular rotation constant and of is the shielding constant of thefreeatom. For boron, aluminum and gallium, the following values have been calculated for af : 202.0,789.9 and 2638.6 ppm, respectively (23, 24). The sign convention used for equation 3 follows that of Ramsey (18) where C is positive if g > 0 and negative if g is < 0. It is important to recognize that, with few exceptions (25), the sign convention must result in a negative sign for the first term in equation 3. Recently, there has been a renewed interest in the accurate calculation of spin-rotation tensors for diatomics using modern quantum chemistry techniques (26, 27). The paramagnetic component of the shielding tensor along the molecular axis is zero; thus a can be accurately calculated by ab initio methods. Flygare (22) has shown that, to a good approximation: p
N
x
tom
tom
±
N
N
]
d
σ = o « o υ
||
u
||
d
atom
(4) v
'
In order to make a rigorous comparison between calculated and experimental shielding tensors, it is necessary to correct the calculated shielding for rovibrational aver aging (28-33). Typically, ab initio calculations are carried out on an isolated rigid Facelli and de Dios; Modeling NMR Chemical Shifts ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
262 molecule at the equilibrium geometry, while the spin-rotation tensor, which is used to obtain o , is a weighted average over the rotational and vibrational coordinates of the molecule. Generally, spin-rotation constants are measured for molecules in their ground vibrational state. For diatomic molecules, one can estimate vibrational corrections using the following expressions (28-31): ±
where o is the calculated shielding at r , and/T) and g(T) are defined as: e
e
=
1
77-5 e~
+
rcoth — —
e
=
T7"T
— e
u g ( T )
+ —
e
(6) e
n
( hciù \ c o t h
W
(?)
where i? , ω and a are the usual molecular spectroscopic constants and μ is the reduced mass (34). Recent reports of spin-rotation constants for aluminum(I) chloride (35) and aluminum® isocyanide (36) have made possible the comparison of "experimental" and ab initio calculated shielding results. If one were able to measure the A l chemical shift of one or both these compounds, it would be possible, in principle, to establish an abso lute shielding scale for aluminum; however, the high reactivity of these compounds has so far precluded such measurements. High-resolution microwave measurements have also been recently carried out on A1H (37); however, analysis of the data did not consider the A l spin-rotation interaction (vide infra). There are numerous reports in the literature involving ab initio calculations o f A l nuclear shielding (10,38-44). Of particular relevance to this work are the results of Gauss et al. (42) where ab initio calculations of isotropic aluminum shielding constants for A1H, A1F and A1C1 using self-consistent field (SCF) and Moller-Plesset (MP2) methods are presented. As well, the relationship between the HOMO-LUMO gap and isotropic values of the nuclear shielding constants was demonstrated. Calculations of aluminum shielding constants for A1X " (X = H , F, CI, Br, or I) have shown that inclusion of the spin-orbit interaction improves considerably the agreement between experimental and calculated results (44), particularly for the heavier halides. e
ε
e
27
2 7
27
4
Computational Details. Restricted Hartree-Fock (RHF) calculations were carried out using Gaussian 94 (45) and ACES II (46) on an I B M RISC/6000 computer. The gauge independent atomic orbitals (GIAO) method was used for the shielding calculations (47). A l l second-order many-body perturbation theory (MBPT2, also referred to as MP2) cal culations were performed with ACES II (46).
Facelli and de Dios; Modeling NMR Chemical Shifts ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
263 The bond lengths employed for the calculations are summarized in Table I. For A1H, A1F, A1C1 and A1NC, a detailed study of the basis set dependence of the nuclear shielding was carried out, the smallest basis set being 6-31G and the largest being 6311++G(3df,3pd). For the largest basis set, the notation indicates that the 6-311G basis set is augmented by three sets of d and f polarization functions in addition to diffuse func tions for atoms other than hydrogen for which three sets of ρ and d polarization functions and diffuse functions are employed. Calculations were performed at both RHF and MP2 levels of theory for A1H, A1F, A1C1 and A1NC. First and second derivatives of the shield ing with respect to internuclear separation were estimated by calculating the shielding at r ± 0 . 0 1 Â. For comparative purposes, calculated boron and gallium shielding tensors of their respective hydrides and halides were also investigated at the RHF level of theory with the 6-31 lG(d,p) basis set, which was the largest available for all the elements involved, with the exception of iodine for which a [10s,8p,4d] basis set (48) with two sets of f functions (orbital exponents of 4.0 and 1.0) (49) was used. Calculations were also performed at the MP2 level, except for molecules containing Ga, Br and I. e
Results and Discussion. The calculated aluminum shielding tensors for A1H, A1F, A1C1 and A1NC for a variety of basis sets are presented in Table II. This particular family of basis sets was chosen as it is the one most commonly used in shielding calculations, espe cially for large systems. The "experimental" magnetic shielding tensors are obtained from
Table I : Geometries Employed in Aluminum Shielding and E F G Tensor Calculations Reference Bond Length(s) (À) Molecule (50) 1.645 362 2 A1H (51) 1.645 366 92 (52) 1.654 360 A1F (53) 2.130 11 A1C1 (54) 1.849 (A1,N) 1.171 (N, C) A1NC optimized 1.8785 (A1,N) 1.1938 (N,C) (53) 2.294 80 AlBr (53) 2.537 09 All BH BF BC1 BBr BI
1.232 4 1.262 1.716 1.888 2.10
(55) (55) (56) (55) (57)
GaH GaF GaCl GaBr Gal
1.662 120 7 1.774 361 9 2.201 690 2.352 48 2.574 673
(58) (52) (55) (55) (59)
Facelli and de Dios; Modeling NMR Chemical Shifts ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
a
Table II: Aluminum Magnetic Shielding Tensors for A1H, A1F, A1C1 and A l N C MP2 molecule and RHF basis set o o °~iso °Ί
